Product Formation

A classic study by Luedeking and Piret (1959) considered
the relationship of cell growth to product formation. When the cells or some
constituent of cells that is proportional to cell mass is the product, the
rate of formation of product directly relates to the rate of growth. Many
other products are known that have zero or a small rate of formation until
growth ceases. It is useful to think of this as the cell using resources to
grow until some important nutrient such as the sugar falls to a low
concentration. For several years, lactose was thought to be essential for
the penicillin fermentation. It was found that lactose (glucose and galactose
linked to form a disaccharide) was hydrolyzed at a rate that supplied sugar
for the synthesis of the antibiotic but did not provide concentrations that
stimulated growth. Dramatic improvements in titer were realized by abandoning
lactose and feeding glucose fast enough for optimum synthesis of penicillin
while avoiding concentrations that gave growth instead. Actual situations, then,
range from entirely growth-associated product formation, through cases where
product formation is partially growth-associated, to cases where product
formation is an alternative to growth.

Luedeking and Piret proposed the following simple equation:

When tested with the microbial process for producing lactic acid, this
equation fit actual data very well. This was somewhat fortuitous because
the agreement is not so good with some other processes. Probably
alpha and beta do
not remain constant as the physiological age of the cells or the conditions
of the process change. Nevertheless, the concept of distinguishing the
relationship of product formation to growth rate is sound.
Simulation exercise for graphing a batch process